A remark on C2 infinity-harmonic functions
Files
Date
2006-10-06
Authors
Yu, Yifeng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper, we prove that any nonconstant, C2 solution of the infinity Laplacian equation uₓiuₓj uₓiₓj = 0 can not have interior critical points. This result was first proved by Aronsson [2] in two dimensions. When the solution is C4, Evans [6] established a Harnack inequality for |Du|, which implies that non-constant C4 solutions have no interior critical points for any dimension. Our method is strongly motivated by the work in [6].
Description
Keywords
Infinity Laplacian equation, Infinity harmonic function, Viscosity solutions
Citation
Yu, Y. (2006). A remark on C2 infinity-harmonic functions. <i>Electronic Journal of Differential Equations, 2006</i>(122), pp. 1-4.